CAT 2025 Formula Sheet: Key Quantitative Aptitude Formulas for Success

CAT 2025 Formulae: The CAT 2025 formula sheet is a powerful and strategic tool for aspirants targeting high scores in the Quantitative Aptitude section. It includes all vital formulas from Arithmetic, Algebra, Geometry, Trigonometry, and the Number System. Designed for quick revision and smart learning, this CAT formula sheet enhances concept clarity, boosts calculation speed, and improves performance in CAT mock tests. Regular use of this Quant formula sheet for CAT 2025 can significantly increase accuracy and help you crack the exam more efficiently.

This Story also Contains

1. Overview of CAT 2025 Quantitative Aptitude section
2. Key Features of the CAT Formula Sheet
3. CAT Important Formulas of Geometry
4. CAT Important Formulas of Trigonometry
5. Quantitative Aptitude Formulae for CAT 2025
6. Why is the CAT 2025 Formulae Important?
7. How to Use the CAT 2025 Formulae Sheet for Exam Preparation?
8. CAT 2025 Quantitative Aptitude Preparation
9. CAT Preparation 2025 Important Books

Overview of CAT 2025 Quantitative Aptitude section

The CAT 2025 Quantitative Aptitude section is one of the most challenging sections of the MBA entrance exam. This is mainly due to the high difficulty level and tricky questions that are asked in it. However, candidates can master these topics from CAT 2025 Syllabus with the help of the CAT 2025 Formula Sheet.

Practising these formulas regularly helps to improve your speed in calculations and gain an edge over other candidates. Whether you are just starting to prepare for the CAT 2025 or getting ready for the final exam. It is important to make these quantitative formulas a key part of your study plan.

Key Features of the CAT Formula Sheet

The CAT Formula Sheet is a strategic tool designed to help aspirants quickly revise and recall essential formulas across key topics like Arithmetic, Algebra, Geometry, and Trigonometry. It enhances exam preparation by offering structured, topic-wise Quantitative Aptitude formulas that improve problem-solving efficiency and accuracy during the CAT exam.

1. Topic-Wise Segregation for Focused Preparation
The CAT formula sheet is systematically divided into core Quantitative Aptitude topics such as Arithmetic, Algebra, Geometry, Trigonometry, and Number System. This organised structure helps aspirants target specific areas during revision.

2. Comprehensive and Exam-Relevant Formulas
It includes all important formulas for CAT that are frequently tested in past exams. Only high-utility formulas that directly aid in solving Quant questions are included. It helps students avoid distractions and concentrate on formulas with the highest exam relevance and scoring potential.

3. High-Visibility Layout for Quick Recall
Designed with readability in mind, the sheet uses bold headings, colour-coded sections, and concise formats to make it visually appealing and easy to scan. This makes it highly effective for last-minute CAT 2025 revision, especially when time is limited and quick recall is essential.

4. Quick Revision-Friendly Format
Ideal for daily practice and mock test preparation, the formula sheet allows aspirants to revise all crucial formulas quickly. It is vital for mastering speed-based problem-solving techniques required for the CAT Quantitative Aptitude section.

5. Updated According to the Latest CAT Exam Pattern
The formula sheet is regularly updated based on the latest trends, question formats, and difficulty levels observed in recent CAT exams. This ensures that aspirants are not only revising the right formulas but also staying aligned with the current CAT exam syllabus.

CAT Important Formulas of Geometry

Mastering important geometry formulas is crucial for cracking the CAT exam, as geometry is a key topic in the Quantitative Aptitude section. The following section covers all essential CAT geometry formulas, including areas, polygons, angles, and properties of triangles and circles to help you solve problems quickly and accurately.

CAT Important Formulas of Trigonometry

Trigonometry plays a vital role in the CAT Quantitative Aptitude section, making it essential to learn and memorise key formulas. This comprehensive list of important CAT trigonometry formulas helps aspirants solve complex problems with speed, accuracy, and confidence during the exam.

1. Basic Trigonometric Ratios

These are defined in relation to a right-angled triangle:

• $ \sin \theta = \frac{\text{Opposite side}}{\text{Hypotenuse}} $

• $ \cos \theta = \frac{\text{Adjacent side}}{\text{Hypotenuse}} $

• $ \tan \theta = \frac{\text{Opposite side}}{\text{Adjacent side}} $

• $ \csc \theta = \frac{\text{Hypotenuse}}{\text{Opposite side}} $

• $ \sec \theta = \frac{\text{Hypotenuse}}{\text{Adjacent side}} $

• $ \cot \theta = \frac{\text{Adjacent side}}{\text{Opposite side}} $

2. Pythagorean Identities

• $ \sin^2 \theta + \cos^2 \theta = 1 $

• $ 1 + \tan^2 \theta = \sec^2 \theta $

• $ 1 + \cot^2 \theta = \csc^2 \theta $

3. Trigonometric Functions of Negative Angles

• $ \sin(-\theta) = -\sin \theta $

• $ \cos(-\theta) = \cos \theta $

• $ \tan(-\theta) = -\tan \theta $

• $ \csc(-\theta) = -\csc \theta $

• $ \sec(-\theta) = \sec \theta $

• $ \cot(-\theta) = -\cot \theta $

4. Angle Sum and Difference Formulas

• $ \sin(A + B) = \sin A \cos B + \cos A \sin B $

• $ \sin(A - B) = \sin A \cos B - \cos A \sin B $

• $ \cos(A + B) = \cos A \cos B - \sin A \sin B $

• $ \cos(A - B) = \cos A \cos B + \sin A \sin B $

• $ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} $

• $ \tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B} $

Quantitative Aptitude Formulae for CAT 2025

Quantitative Aptitude formulas form the foundation of the Quantitative Aptitude section in the CAT 2025 exam. Here are some important CAT 2025 quant section-wise formulae for CAT 2025 preparation:

Arithmetic

The Arithmetic section is the most important section in the Quantitative Aptitude Section, which is also useful to solve the Data Interpretation problems. Following are some 50+ Important Formulas for CAT Preparation of this section which are given in this CAT Formula Sheet:

Percentage

Following are some Important CAT Formulas of percentage:

$ \text{X is what percentage of Y} = \frac{X}{Y} \times 100% $

$ \text{X is what percentage more/less than Y} = \frac{|X - Y|}{Y} \times 100% $

$ \text{If X is } a% \text{ more than Y, then } X = Y \times \left( \frac{100 + a}{100} \right) $

$ \text{If X is } a% \text{ less than Y, then } X = Y \times \left( \frac{100 - a}{100} \right) $

Shortcut Formulas

Following are some formulas which can be used as CAT Quant Formulae:

Profit & Loss:

Following are some Important CAT Formulas of this topic:

Shortcut Formulas

Cheat Sheet for the preparation and exam point of view:

Simple Interest (S.I.) & Compound Interest (C.I.):

Following are some basic and Important Formulas for CAT 2025 related to Simple Interest and Compound Interest:

Shortcut Formulas

Following are some formulas which can be used as CAT Quant Formula Cheat Sheet for the preparation and exam point of view:

Time, Speed & Distance:

Following are some basic and Important Formulas for CAT 2025 related to Time, Speed and Distance:

Trains:

Boat & Streams:

Clocks:

Shortcut Formulas

Following are some Quantitative Aptitude Formulas which can be used as a CAT Quant Formula Cheat Sheet for the preparation and exam point of view:

1. If the distance covered in each stage of the journey is the same, but speeds are different, then the average speed is the harmonic mean of the different speeds.

Ex: If distance between point A to B and B to C are same and are covered with the speed of $s_1$ and $s_2$ respectively. Then-

$ \text{Average Speed} = \frac{2 S_1 S_2}{S_1 + S_2} $

2. If the time taken in each stage of journey is same, but speeds are different then, the average speed is the average of the different speeds.

Ex: If time taken between points A to B and B to C is same and these distances are covered with the speed of $s_1$ and $s_2$ respectively. Then-

$ \text{Average Speed} = \frac{S_1 + S_2}{2} $

3. If two people start running on a circular track of length D km in the same direction from the same point with speeds a & b kmph, then-

(i) Time taken in first meeting$ = \frac{D}{|a - b|} \text{ hr} $

(ii) Time taken to meet again at the starting point$ = \text{LCM} \left( \frac{D}{a}, \frac{D}{b} \right) $

(iii) Number of distinct meeting points$ = |x - y| $

{x & y are the simplified ratio of speeds, Ex: If speeds a & b are 12 kmph & 9 kmph

respectively, then- x: y = 12: 8 = 3: 2; So, x = 3 & y =2}

4. If two people start running on a circular track of length D km in the opposite direction from the same point with speeds a & b kmph, then-

(i) Time taken in first meeting = D|a+b| hr.

(ii) Time taken to meet again at the starting point = LCM (Da ,Db) hr.

(iii) No. of Distinct meeting Points = |x + y|

{x & y are the simplified ratio of speeds}

5. If a person P starts from A and heads towards B and another person Q starts from B and heads towards A and they meet after a time 't' then, $t=(x.y)$

[where x = time taken (after meeting) by P to reach B and y = time taken (after meeting) by Q to reach A]

6. If the speed of the boat downstream is u kmph and the speed of the boat upstream is v kmph, then-

$ \text{Speed of the boat in still water} = \frac{u + v}{2} \text{ kmph} $

$ \text{Rate of stream} = \frac{u - v}{2} \text{ kmph} $

Geometry

The Geometry section is the lengthiest section in the Quantitative Aptitude Section which has lots of properties and formulas. Following are 50+ Important Formulas for CAT Preparation of this section which are given in this CAT Formula Sheet:

1. Triangles:

Properties of Triangles:

1. The sum of all interior angles in a triangle is 180° and Exterior angles is 360°.

2. The sum of any two sides is always greater than the third one and the difference of any two sides is less than the third one.

Let a,b,c are the sides of triangles, then

|b-c| < a < b + c

3. In a Scalene Triangle the greatest side is always greater than the one-third of perimeter and less than half of the perimeter.

• Let a,b,c are the sides of triangles and a is the greatest side of the triangle. The perimeter of the triangle is P.

P/3 < a < P/2

Ex: In a scalene triangle ABC, the perimeter of the triangle is 24 cm and all sides are integers.

Sol: Let a,b,c are sides of a triangle, and a is the greatest side.

$24/3 < a < 24/2$

$8 < a < 12$

So, all possible values are 9,10,11 cm.

4. Let a,b,c are sides of a triangle, and a is the greatest side.

If $a^2<b^2+c^2$

Then triangle is an acute angled triangle

If $a^2=b^2+c^2$

Then triangle is a Right-angled triangle= Pythagoras theorem

If $a^2>b^2+c^2$

Then triangle is an Obtuse angled triangle

5. (Here D is the midpoint of the AC side or AD = DC).

6. Length of the Median-

$ BD = \frac{1}{2} \sqrt{2(AB^2 + BC^2) - AC^2} $

7. 3 (Sum of squares of sides) = 4 (Sum of squares of medians)

$ 3(a^2 + b^2 + c^2) = 4(M_a^2 + M_b^2 + M_c^2) $

{Where a,b,c are sides of triangle and Ma, Mb, Mc are medians of the triangle}

8. In a right-angle triangle, Median of Hypotenuse= Hypotenuse/2

$CD = \frac{AB}{2}$

9. If all the medians are drawn in the triangle, then the 6 small triangles are generated in the triangle, which are equal in the Area.

Area of Triangle:

1. Heron’s Formula

If all sides of a triangle are given. Let a,b,c are sides of triangle-

$ \text{Area} = \sqrt{s(s - a)(s - b)(s - c)} \quad \text{where } s = \frac{a + b + c}{2} $ where s is the semiperimeter.

2. If two sides and one included angle is given-

Area = ½ x Product of given sides x Sin(given included angle)

$ \text{Area} = \frac{1}{2} \times a \times b \times \sin C $

{ex: sides a, b are given and included angle C is given}

3. If a side and its respective Altitude (perpendicular drawn on a side from the opposite vertex) is given, then-

Area of the triangle = ½ x Base x Height (Altitude)

Shortcut Formulas

1. $ \text{Area of an equilateral triangle} = \frac{\sqrt{3}}{4} a^2 $

2. $ \text{Height (Altitude) of an equilateral triangle} = \frac{\sqrt{3}}{2} a $

3. $ \text{Area of a triangle} = r \times s \quad \text{(where $r$ is inradius and $s$ is semi-perimeter)} $

4. $ \text{Area of a triangle} = \frac{abc}{4R} \quad \text{(where $a$, $b$, $c$ are sides and $R$ is circumradius)} $

Quadrilaterals:

3. Circle:

$ \text{Circumference of a circle} = 2\pi r $

$ \text{Area of a circle} = \pi r^2 $

Semi-circle

$ \text{Circumference of a semi-circle} = \pi r $

$ \text{Perimeter of a semi-circle} = \pi r + 2r $

$ \text{Area of a semi-circle} = \frac{\pi r^2}{2} $

Sector & Segment of circle

{OAXC is called the sector of the circle & AXC is called the segment}

• $ \text{Length of arc AXC} = \frac{\theta}{360} \times 2\pi r \quad \text{(where } r \text{ is the radius)} $

• $ \text{Area of sector OAXC} = \frac{\theta}{360} \times \pi r^2 $

• $ 2 \times \text{Area of sector} = \text{Length of arc} \times \text{Radius} $

• $ \text{Area of segment AXC} = \text{Area of sector OAXC} - \text{Area of } \triangle OAC $

• $ A = \frac{\theta}{360} \pi r^2 - \frac{1}{2} r^2 \sin \theta $

Where:

• $\theta$ is the angle subtended at the center (in degrees)

• $r$ is the radius of the circle

Common Tangent

PQ & RS are the direct common tangents of the circle, which are equal in length. Length of direct common tangent (L)-

$L^2=d^2–(r_1−r_2)^2$

{d = distance between centers of circle, $r_1,r_2$ are radius of circle}

1. PQ & RS are the transverse common tangents of the circle, which are equal in length. Length of transverse common tangent (L)-

2. $ L^2 = d^2 - (r_1 + r_2)^2 $

Where:

• $L$ is the length of the direct common tangent,

• $d$ is the distance between the centers of the two circles,

• $r_1$ and $r_2$ are the radii of the two circles.

Mensuration:

Algebra

The Algebra section is a critical part of the Quantitative Aptitude section in the CAT exam. Below are over 50 important formulas for CAT preparation in this section, which are provided in this comprehensive CAT Formula Sheet:

1. Quadratic Equations

1. General Quadratic equation will be in the form of $??^2+??+?=0$

2. Values of ‘x’ which satisfies the equation are called roots of the equation. To find the roots the Shreedhara Acharya's Formula is used.

Roots of the equation,

$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

$ \text{Sum of the roots} = -\frac{b}{a} $

$ \text{Product of the roots} = \frac{c}{a} $

$ \text{Difference of the roots} = \frac{D}{a} \quad \text{where } D = b^2 - 4ac $

If $ D > 0 $, then the roots of the equation are real and distinct.

i. If D is perfect square, then roots will be rational; ex: x = 1,6

ii. If D is non-perfect square, then roots will be irrational or conjugate surds

ex: $x = 3-\sqrt{5}, 3+\sqrt{5}$

If $ D = 0 $, then the roots of the equation are real and equal.

If $ D < 0 $, then the roots of the equation are imaginary and distinct.

$ y = ax^2 + bx + c \quad \text{where } a > 0 $

• For $ y = ax^2 + bx + c $, if $ a > 0 $, the minimum value occurs at $ x = \frac{-b}{2a} $ and is given by:
  $ y = \frac{-D}{4a} \quad \text{(Minimum value)} $

• For $ y = ax^2 + bx + c $, if $ a < 0 $, the maximum value occurs at $ x = \frac{-b}{2a} $ and is given by:
  $ y = \frac{-D}{4a} \quad \text{(Maximum value)} $

Where $ D = b^2 - 4ac $ is the discriminant.

If the roots of the quadratic equation are $a$ and $b$, then the quadratic equation is:

$ x^2 - Sx + P = 0 \quad \text{where } S = a + b \text{ and } P = ab $

That is:

$ x^2 - (a + b)x + ab = 0 $

Progression & Series

In this chapter there are three types of progression, which are-

1. Arithmetic Progression

2. Geometric Progression

3. Harmonic Progression

Arithmetic Progression (A.P.)

If a is the first term and d is the common difference then the Arithmetic Progression (A.P.). can be written as-

• $ a,\ a + d,\ a + 2d,\ a + 3d,\ \ldots $

Where:

$a$ = first term

$d$ = common difference

Nth term of the A.P. –

$T_n=a+(n−1).d$

Here $n$ is the no. of terms

Sum of the n terms of the A.P. ($S_n$) = Average of all the terms x no. of terms(n)

Average of the terms can be found out easily

• If no. of terms is odd then the middle term will be the average

Ex: 2,5,8,11,14 are the terms of the A.P. then middle term 8 is the average

So, the sum = avg. x n = 8 x 5 = 40

• If no. of terms is even then the average of middle terms will be the average of the A.P.

$S_n=\frac{n}{2}[2a+(n−1)d]$

Shortcut Formulae

$ S_n = \frac{n}{2}(a + l) \quad \text{(where } a = \text{first term, } l = \text{last term, } n = \text{number of terms)} $

$ n = \frac{l - a}{d} + 1 \quad \text{(number of terms in A.P.)} $

Geometric Progression (G.P.)

If a is the first term and r is the common ratio then the Geometric Progression (G.P.) can be written as-

$a,a.r,a.r^2,a.r^3,\ldots$

Nth term of the G.P. –

$T_n=a.r^{n−1}$ where n is the no. of terms

Sum

• $ S_\infty = \frac{a}{1 - r} \quad \text{if } |r| < 1 $

• If $ r < 1 $:
  $ S_n = a \cdot \frac{1 - r^n}{1 - r} $

• If $ r > 1 $:
  $ S_n = a \cdot \frac{r^n - 1}{r - 1} $

Where:

$a$ = first term

$r$ = common ratio

$n$ = number of terms

Sum of infinite terms of the G.P.-

$ S_\infty = \frac{a}{1 - r} \quad \text{if } |r| < 1 $

Where:

• $a$ = first term

• $r$ = common ratio

• $|r| < 1$ ensures the series converges.

Shortcut Formulas

If there are odd no. of terms in a G.P., then the product of all terms are equal to the nth power of the middle term.

e.g. 2,6,18,54,162 are the terms of a G.P.

Then the products of all the terms = 185

Harmonic Progression (H.P.)

If $ a, b, c $ are in A.P., then $ \frac{1}{a}, \frac{1}{b}, \frac{1}{c} $ are in Harmonic Progression (H.P.).

$ \text{n-th term of the H.P.} = \frac{1}{\text{n-th term of the corresponding A.P.}} $

Series

Sum of first $n$ natural numbers:
$ 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}{2} $

Sum of squares of first $n$ natural numbers:
$ 1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n+1)(2n+1)}{6} $

Sum of cubes of first $n$ natural numbers:
$ 1^3 + 2^3 + 3^3 + \cdots + n^3 = \left( \frac{n(n+1)}{2} \right)^2 $

Sum of first $n$ natural odd numbers:
$ 1 + 3 + 5 + \cdots + (2n - 1) = n^2 $

Sum of squares of first $n$ even numbers:
$ 2^2 + 4^2 + 6^2 + \cdots + (2n)^2 = \frac{2n(n+1)(2n+1)}{3} $

Sum of squares of first $n$ odd numbers:
$ 1^2 + 3^2 + 5^2 + \cdots + (2n - 1)^2 = \frac{n(2n+1)(2n-1)}{3} $

Indices & Surds

Product Rule:

$ a^m \cdot a^n = a^{m+n} $

Quotient Rule:

$ \frac{a^m}{a^n} = a^{m - n} $

Power of a Power:

$ (a^m)^n = a^{mn} $

Power of a Product:

$ (ab)^n = a^n \cdot b^n $

Power of a Quotient:

$ \left( \frac{a}{b} \right)^n = \frac{a^n}{b^n} $

Negative Exponent:

$ a^{-n} = \frac{1}{a^n} $

Shortcut Formulae

$ \prod_{n=1}^{\infty} a = \lim_{n \to \infty} a_n $

Logarithmic Rules and Properties

Definition of Logarithm:

$ \log_b a = x \iff b^x = a $

Log of 1:

$ \log_b 1 = 0 \quad \text{(for any base } b > 0,\ b \ne 1) $

Log of the base itself:

$ \log_b b = 1 $

Log of a product:

$ \log_b (mn) = \log_b m + \log_b n $

Log of a quotient:

$ \log_b \left( \frac{m}{n} \right) = \log_b m - \log_b n $

Log of a power:

$ \log_b (m^n) = n \cdot \log_b m $

Change of base formula:

$ \log_b a = \frac{\log_k a}{\log_k b} \quad \text{(commonly with base 10 or } e \text{)} $

Base switch rule:

$ \log_a b = \frac{1}{\log_b a} $

Why is the CAT 2025 Formulae Important?

CAT 2025 Formulae is crucial for MBA exam preparation as it compiles essential mathematical formulas and concepts, streamlining study efforts and enhancing exam readiness. This resource not only aids in quick recall but also fosters a deeper understanding of quantitative topics.

• A consolidated formula PDF for CAT allows for focused study sessions. It also reduces the time spent searching for formulas across various resources.

• Regular use of the CAT formula PDF helps in developing quick problem-solving techniques. This is essential for tackling the time constraints of the CAT exam.

• A CAT formula sheet helps candidates to do quick revisions before the examination.

• Familiarity with formulas leads to fewer mistakes during the exam. This boosts both confidence and accuracy before the examination.

• Understanding which formulas are most relevant helps candidates prioritise questions. This leads to a more strategic approach and helps in maximising their scores.

How to Use the CAT 2025 Formulae Sheet for Exam Preparation?

A CAT 2025 formula sheet is an advanced tool for precision-driven preparation, enabling strategic revision and targeted practice. Read on to know about the ways in which you can use the CAT 2025 formula PDF for the examination.

• Dedicate specific time slots each day to review and recite formulas. This reinforces memory retention and ensures familiarity with key concepts.

• Pair each formula with example problems to understand its application. This enhances comprehension and enables quicker recall during the exam.

• Use the formula sheet while attempting the CAT 2025 mock tests. This allows for real-time application and helps to identify areas needing further practice.

• Create visual aids or mind maps from the formula sheet to connect related concepts, facilitating deeper understanding and quicker retrieval during problem-solving.

• Refine the formula sheet regularly by adding new insights, shortcuts, or variations encountered during practice.

CAT 2025 Quantitative Aptitude Preparation

Whether you're reviewing concepts or tackling practice problems, having a CAT formulas cheat sheet at your fingertips provides immediate access to vital quantitative formulas. This resource is essential for streamlining your preparation, as it gathers all necessary CAT 2025 quant formulae, enhancing both efficiency and effectiveness.

Careers360 has developed a comprehensive ebook featuring the top 100 facts. It helps candidate by boosting their preparation for the CAT 2025 quantitative aptitude section. It also contains essential formulas relevant to the CAT QA section. Candidates can download and study this ebook for effective CAT Quantitative Aptitude 2025 exam preparation.

CAT 2025 Quantitative Aptitude Syllabus

The CAT Quantitative Aptitude Syllabus is one of the most crucial resources that candidates must keep handy before commencing their preparations. The CAT Syllabus 2025 consists of topics that are asked during the examination. Refer to the table below to get the updated CAT 2025 Quantitative Aptitude syllabus.

CAT Preparation 2025 Important Books

Choosing the right set of books during CAT preparation 2025 is very essential to excel in the examination. These books offer conceptual clarity for different topics and also provide ample practice questions. Here is a list of important books on CAT 2025 Quantitative Aptitude.